A Folk Theorem for Indefinitely Repeated Network Games

We consider a repeated game in which players, considered as nodes of a network, are connected. Each player observes her neighbors' moves only. Thus, monitoring is private and imperfect. Players can communicate with their neighbors at each stage; each player, for any subset of her neighbors, sends the same message to any player of that subset. Thus, communication is local and both public and private. Both communication and monitoring structures are given by the network. The solution concept is perfect Bayesian equilibrium. In this paper we show that a folk theorem holds if and only if the network is 2-connected for any number of players.